The migration of conversational AI agents across different embodiments in order to maintain the continuity of the task has been recently explored to further improve user experience. However, these migratable agents lack contextual understanding of the user information and the migrated device during the dialog conversations with the user. This opens the question of how an agent might behave when migrated into an embodiment for contextually predicting the next utterance. We collected a dataset from the dialog conversations between crowdsourced workers with the migration context involving personal and non-personal utterances in different settings (public or private) of embodiment into which the agent migrated. We trained the generative and information retrieval models on the dataset using with and without migration context and report the results of both qualitative metrics and human evaluation. We believe that the migration dataset would be useful for training future migratable AI systems.